Strong Disjointness of Frames and Constructions of Tight Frames
Xun Xiang GUO
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School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P. R. China
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文章历史+
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出版日期
2013-08-23
2014-12-31
2015-07-15
发布日期
2015-07-15
摘要
Hilbert空间上框架的分离性概念是由 Han 与 Larson首先提出的. 分离框架有很多有用的性质.本文利用强分离紧框架来构造出新的紧框架. 特别地,我们将给出一些充分或充要条件使得正规紧框架的算子系数的线性组合是某些特殊的紧框架.并给出一个框架存在界满足一定条件的紧对偶框架的充要条件.最后还讨论了实Hilbert空间中的一些相关问题.
Abstract
Disjointness of frames in Hilbert spaces was firstly introduced by Han and Larson. There are lots of useful properties on disjoint frames. In this paper, firstly we use strongly disjoint tight frames to construct new tight frames. In particular, we give some sufficient or some sufficient and necessary conditions such that the linear combinations of normalized tight frames with operator coefficients to be certain tight frames. We also give a necessary and sufficient condition such that a frame has tight dual frame with certain frame bound. Then we study the corresponding problems in real Hilbert spaces.